2-Complex Symmetric Composition Operators on H2

Abstract

In this paper, we study 2-complex symmetric composition operators with the conjugation J, defined by Jf(z)=(f(z¯))¯, on the Hardy space H2. More precisely, we obtain the necessary and sufficient condition for the composition operator Cϕ to be 2-complex symmetric with J when ϕ is an automorphism of D. We also characterize 2-complex symmetric with J when ϕ is a linear fractional self-map of D.

3-Complex Symmetric and Complex Normal Weighted Composition Operators on the Weighted Bergman Spaces of the Half-Plane

“…It is clear that a 1-complex symmetric operator is just the complex symmetric operator. Recently, Hu et al in [22] characterized 2-complex symmetric composition operators on Hardy space on the unit disk. From [18], or direct proof, we see that complex symmetric operators are also 2-complex symmetric operators.…”